Using the [1]} model,
[2]} describe the magnetospheric accretion flow
as originating from the CPD between the inner (or truncation) radius \(R_\mathrm {i}\)  and the outer radius \(R_\mathrm {o}=R_\mathrm {i}+W_r\) , where \(W_r\)  is the width of the flow at the launching point.
With these definitions,
the axisymmetric angles on the planet covered by accretion
are given by \(\sin ^2\theta _{\mathrm {i},\mathrm {o}}=R_{\mathrm {p}}/R_{\mathrm {i},\mathrm {o}}\)  [1]}.
From Equation (REF ), the filling factor is
\(f_{\mathrm {fill}}= \sqrt{1-\frac{R_{\mathrm {p}}}{R_\mathrm {i}+W_\mathrm {r}}} - \sqrt{1-\frac{R_{\mathrm {p}}}{R_\mathrm {i}}}.\) 
